Question 1

An incandescent lightbulb is rated at 100 Watts when plugged into a 110 V-rms household outlet. Calculate the resistance of the filament and the rms current.

Accepted Answer

Given, Power, P = 100 W
Voltage, V = 110 V
We know that, Power P = (V^2)/R
Therefore, R = (V^2)/P = (110^2)/100 = 121 Ω
Now, we can find the rms current using the formula I = V/R = 110/121 = 0.91 A (rms)
Therefore, the answer is D) 121Ω, 0.91 A (rms)

Question 2

If the input to an RLC series circuit is V = V_m cos ωt, then the current in the circuit is

Accepted Answer

D

Question 3

Inductive reactance X_L is given by

Accepted Answer

Inductive reactance is given by the formula $X_L = L\omega$, where $L$ is the inductance in henrys and $\omega$ is the angular frequency in radians per second.

Question 4

A 2.0-μF capacitor in series with a 2.0-kΩ resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit.

Accepted Answer

The impedance of the circuit can be calculated using the formula Z = √(R² + Xc²), where R is the resistance and Xc is the reactance of the capacitor.

Since the capacitor has a capacitance of 2.0 μF and is connected to a 60-Hz ac source, the capacitive reactance can be calculated using the formula Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

Xc = 1/(2π(60)(2.0×10^-6)) 
Xc = 1326.2 ohms

The resistance is given as 2.0 kΩ.

Z = √(R² + Xc²) 
Z = √((2.0×10³)² + (1326.2)²) 
Z = 2400 ohms

Therefore, the impedance of the circuit is 2 400 ohms, which is option D.

Question 5

A 10.0-μF capacitor is plugged into a 110 V-rms 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the capacitor?

Accepted Answer

The capacitive reactance XC, in ohms, is given by XC = 1/(2πfC), where f is the frequency in Hz and C is the capacitance in farads. Plugging in the given values, XC = 1/(2π(60)(10.0×10^-6)) = 265.26 ohms. The current through the capacitor is given by I = V/XC, where V is the voltage across the capacitor. Since the voltage source is rms, V = 110 V / √2 = 77.942 V (peak voltage). Therefore, I = 77.942 V / 265.26 ohms = 0.294 A (peak current). The rms value of the current is then given by Irms = I / √2 = 0.294 A / √2 = 0.415 A (rms), which is closest to choice B.

Question 6

A 0.500-H inductor is connected into a 110 V-rms 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the inductor?

Accepted Answer

The answer of A 0.500-H inductor is connected into a...

Question 7

Find the resonant frequency for a series RLC circuit where R = 10Ω, C = 5.00 μF, and L = 2.00 mH.

Accepted Answer

The resonant frequency for a series RLC circuit can be calculated using the formula:

f = 1/(2π√(LC))

where f is the resonant frequency in Hertz (Hz), L is the inductance in Henrys (H), and C is the capacitance in Farads (F).

Substituting the given values into the formula:

f = 1/(2π√(2.00 mH x 5.00 μF))

f = 1/(2π√(2.00 x 10^-3 H x 5.00 x 10^-6 F))

f = 1/(2π√(10^-11))

f = 1/(2π x 10^-6)

f = 1591.55 Hz

Therefore, the resonant frequency for the series RLC circuit is 1.59 kHz, which is best represented by choice B.

Question 8

A 230000 V-rms powerline carries an average power P_avg = 250 MW a distance of 200 km. If the total resistance of the cables is 10 ohms, what is the resistive power loss?

Accepted Answer

The answer of A 230000 V-rms powerline carries an average...

Question 9

At what frequency will a 50.0-mH inductor have a reactance X_L = 700Ω?

Accepted Answer

The answer of At what frequency will a 50.0-mH inductor...

Question 10

The inductance of a tuning circuit of an AM radio is 4.00 mH. Find the capacitance of the circuit required for reception at 1 200 kHz.

Accepted Answer

The answer of The inductance of a tuning circuit of...

Question 11

Capacitive reactance X_C is given by

Accepted Answer

Capacitive reactance is given by the formula 1/ωC, where ω is the angular frequency and C is the capacitance. Therefore, option A is the correct choice.

Question 12

The voltage 8.00 sin (400t) is applied to a series RLC circuit, with R = 200 Ω, L = 0.100 H, and C = 1.00 μF. What are the impedance Z and the phase angle θ?

Accepted Answer

The answer of The voltage 8.00 sin (400t) is applied...

Question 13

An electric heater draws an average power of 1100 Watts when plugged into a 110 V-rms outlet. Calculate the resistance of the heater and the rms current.

Accepted Answer

The resistance of the heater can be calculated using Ohm's law: R = V/I, where V is the voltage and I is the current. The rms current can be calculated using the formula: I = P/V, where P is the power. Substituting the given values, we get: R = 110 V / 10 A = 11 Ω and I = 1100 W / 110 V = 10 A (rms).

Question 14

An ac generator with peak voltage 100 volts is placed across a 10-Ω resistor. What is the average power dissipated?

Accepted Answer

The answer of An ac generator with peak voltage 100...

Question 15

If an R = 1.0-kΩ resistor, a C = 1.0-μF capacitor, and an L = 0.20-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source?

Accepted Answer

The maximum current in an RLC series circuit is determined by the impedance Z, which is calculated using Z = √(R² + (XL - XC)²), where XL = ωL and XC = 1/(ωC). Here, ω = 377 rad/s. Calculate XL = 377 * 0.20 = 75.4 Ω and XC = 1/(377 * 1.0e-6) = 2652.5 Ω. Then, Z = √(1000² + (75.4 - 2652.5)²) ≈ 2777.5 Ω. The maximum current I_max = V_max / Z = 150 / 2777.5 ≈ 0.054 A or 54 mA.

Question 16

The total impedance Z of an RLC circuit driven by an ac voltage source at angular frequency ω is,

Accepted Answer

The answer of The total impedance Z of an RLC...

Question 17

A high-voltage powerline operates at 500000 V-rms and carries an rms current of 500 A. If the resistance of the cable is 0.050Ω/km, what is the resistive power loss in 200 km of the powerline?

Accepted Answer

The answer of A high-voltage powerline operates at 500000 V-rms...

Question 18

At what frequency will a 12-μF capacitor have a reactance X_C = 300Ω?

Accepted Answer

The capacitive reactance (X_C) is given by the formula X_C = 1 / (2πfC). Solving for frequency (f), f = 1 / (2π * 300Ω * 12μF) ≈ 44 Hz.

Question 19

An LC circuit is to have resonant oscillations at 5.0 MHz. Find the value of a capacitor which will work with a 1.0-mH inductor.

Accepted Answer

The answer of An LC circuit is to have resonant...

Question 20

An RLC series circuit has R = 100 ohms, C = 25 μF, and L = 0.16 H. For what angular frequency of an ac voltage is the current flow maximum?

Accepted Answer

The answer of An RLC series circuit has R =...

Quiz 33: Alternating-Current Circuits